Statistically Recognize Faces Based on Hidden Markov Models

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Statistically Recognize Faces Based on Hidden Markov Models. Presented by Timothy Hsiao-Yi Chin Rahul Mody. What is Hidden Markov Model?. Its underlying is a Markov Chain.

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### Statistically Recognize Faces Based on Hidden Markov Models

Presented by

Timothy Hsiao-Yi Chin

Rahul Mody

E6886 Project

### What is Hidden Markov Model?

Its underlying is a Markov Chain.

An HMM, at each unit of time, a single observation is generated from the current state according to the probability distribution, which is dependent on this state.

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Mathematical Notation of HMM
• Suppose that there are T states {S1, …, ST} and the probability between state i and j is Pij. Observation of system can be defined as ot at time t. Let bSi(oi) be the probability function of ot at time t. Lastly, we have the initial probability , i = 1, …, n of Markov chain. Then the likelihood of the observing the sequence o is

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Which probability function of ot?
• In HMM framework, observation o is assumed to be governed by the density of a Gaussian mixture distribution.
• Where k is the dimension of ot, and where oiand

are the mean vector and covariance matrix, respectively

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70%

60%

25%

28%

5%

12%

70%

10%

20%

Example: A Markov Model*

Sunny

Rainy

Snowy

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Represent it as a Markov Model*
• States:
• State transition probabilities:
• Initial state distribution:

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What is sequence o in this example?*
• Sequence o:
• The probability could be computed by the conditional probability:

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Example: A HMM*

5%

70%

80%

20%

20%

Sunny

60%

Rainy

15%

38%

2%

5%

5%

75%

10%

75%

Snowy

20%

45%

5%

50%

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What other parameters will be needed?
• If we can not see what is inside blue circle, what can we actually see?
• Observations:
• Observation probabilities:

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Forward-Backward Algorithm: Forward
• If Observation probability is
• then

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Forward-Backward Algorithm: Backward
• If there is a
• Then
• The Forward-Backward Algorithm tells us that
• for any time t

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Face identification using HMM
• An Observation sequence is extracted from the unknown face, the likelihood of each HMM generating this face could be computed.
• In theory, the likelihood is
• The maximum P(O) can identifies the unknown faces.
• However, it takes too much time to compute.

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Face identification using HMM
• In practice, we only need one S sequence

which maximizes

• This is a dynamic programming optimization procedure.

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Viterbi Algorithm
• Given a S sequence, a dynamic programming approach to solve this problem
• where
• By induction, the max Probability in state i+1 at time t+1 is based on the max probability in state I at time t.

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Algorithm itself
• Initialization

where denotes the collection of that sequence which is based on max

• Recursion:

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Algorithm itself (2)
• Termination
• Sequence constructing from T to t

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Face Detection
• In simple face recognition framework, the picture is assumed to be a frontal view of a single person and the background is monochrome.
• This project assumes that with the techniques of face detection, the performance of face recognition may be better than the approach presented above.

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Acknowledgement
• The authors of this presentation slides would like to give thanks to Dr. Doan, UIUC.

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Reference
• [1] Ferdinando Samaria, and Steve Young, HMM-based architecture for face identification.
• [2] Jia, Li, Amir Najmi, and Robert M. Gray, Image Classification by a Two-Dimensional Hidden Markov Model
• [3] Ming-Hsuan Yang, David J. Kriegman, Narendra Ahuja, Detecting Faces In Images: A survey
• [4] T.K. Leung, M. C. Burl, and P. Perona, Finding Faces in Cluttered Scenes using Random Labeled Graph Matching
• [5] James Wayman, Anil Jain, Davide Maltoni, and Dario Maio, Biometric Systems, Springer, 2005

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